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 引用本文: 彭再云, 李永红. 半严格-G-半预不变凸性与最优化[J]. 应用数学和力学, 2013, 34(8): 836-845.
PENG Zai-yun, LI Yong-hong. Semistrict-G-Semi-preinvexity and Optimization[J]. Applied Mathematics and Mechanics, 2013, 34(8): 836-845. doi: 10.3879/j.issn.1000-0887.2013.08.007
 Citation: PENG Zai-yun, LI Yong-hong. Semistrict-G-Semi-preinvexity and Optimization[J]. Applied Mathematics and Mechanics, 2013, 34(8): 836-845.

## 半严格-G-半预不变凸性与最优化

##### doi: 10.3879/j.issn.1000-0887.2013.08.007

###### 作者简介:彭再云(1980—),男,重庆人,副教授,博士(通讯作者.E-mail: pengzaiyun@126.com).
• 中图分类号: O221.1

## Semistrict-G-Semi-preinvexity and Optimization

• 摘要: 提出了一类新的广义凸函数——半严格-G-半预不变凸函数，它是一类重要的广义凸函数，是半严格预不变凸函数和半严格-G-预不变凸函数的真推广．首先，用例子说明了半严格-G-半预不变凸函数的存在性，并给出例子说明它是与G-半预不变凸函数不同的一类函数；然后，给出了半严格-G-半预不变凸函数的几个基本性质；最后，讨论了半严格-G-半预不变凸函数分别在无约束和带不等式约束的非线性规划问题中的应用，得到了一些最优性结果，并举例验证所得结论的正确性．
•  [1] Schaible S, Ziemba W T.Generalized Concavity in Optimization and Economics[M]. London, UK: Academic Press Inc, 1981. [2] Mishra S K, Giorgi G.Invexity and Optimization, Nonconvex Optimization and Its Applications[M]. 88. Berlin: Spring, 2008.  [3] Hanson M A. On sufficiency of KuhnTucker conditions[J].Journal of Mathematical Analysis and Applications,1981, 80(2): 545-550. [4] Weir T, Mond B. Preinvex functions in multiobjective optimization[J].Journal of Mathematical Analysis and Applications,1988, 136(1): 29-38. [5] Yang X M, Li D. On properties of preinvex functions[J].Journal of Mathematical Analysis and Applications,2001, 256(1): 229-241. [6] Yang X M, Li D. Semistrictly preinvex functions[J].Journal of Mathematical Analysis and Applications,2001, 258(1): 287-308. [7] Antczak T.G preinvex functions in mathematical programming[J].Journal of Computational and Applied Mathematics,2008, 217(1): 212-226. [8] Antczak T. New optimality conditions and duality results of G-type in differentiable mathematical programming[J].Nonlinear Analysis: Theory, Methods & Applications,2007, 66(7): 1617-1632. [9] Peng Z Y. Semistrictly G-preinvexity and its applications[J].Journal of Inequalities and Applications,2012, doi: 10.1186/1029-242X-2012-198. [10] 彭再云, 周选林, 赵勇. 强-G-预不变凸函数的性质及应用[J]. 重庆师范大学学报（自然科学版）, 2012, 29(4): 12-17.(PENG Zai-yun, ZHOU Xuan-lin, ZHAO Yong. Characteristics and applications of strongly G-preinvex functions[J]. Journal of Chongqing Normal University (Natural Science Edition),2012, 29(4): 12-17. (in Chinese)) [11] Yang X Q, Chen G Y. A class of nonconvex functions and prevariational inequalities[J].Journal of Mathematical Analysis and Applications,1992, 169(2): 359-373. [12] Peng Z Y, Chang S S. Some properties of semi-G-preinvex functions[J]. Taiwan J Math,2013, 17(3): 873-884. [13] 彭再云, 孔祥茜. 强-G-半预不变凸性与非线性规划问题[J]. 广西师范大学学报 (自然科学版）,2013, 31(1): 48-53.(PENG Zai-yun, KONG Xiang-xi. Strongly semi-G-preinvexity and nonlinear programming[J].Journal of Guangxi Normal University (Natural Science Edition),2013, 31(1): 48-53. (in Chinese)) [14] 彭再云, 孔祥茜. 强-G-半预不变凸函数及其性质[J]. 重庆师范大学学报(自然科学版), 2013,30(2): 1-6.(PENG Zai-yun, KONG Xiang-xi. Strongly semi-G-preinvex functions and its properties[J].Journal of Chongqing Normal University (Natural Science Edition),2013, 30(2): 1-6. (in Chinese))

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##### 出版历程
• 收稿日期:  2013-05-07
• 修回日期:  2013-05-28
• 刊出日期:  2013-08-15

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